Of principal note is al-Kitab al-mukhtasar fi hisab al-jabr wa'l-muqabala2,
a collection of techniques of symbol manipulation. It is unclear
how many of these techniques he invented himself, and how many he adopted
from earlier (including Indian and Ancient Greek) mathematicians.

As al-jabr was a really about strategies for solving mathematical
problems, his name, or rather a corruption of it, "algorithm", became
associated with such strategies.

John Napier may have invented the word logarithm to be parallel with
"algorithm". He never explained where he got the word from; another
mathematician, Henry Briggs, ascribes a Greek origin to the word.

He also published Kitab surat al-ard4, a gazetteer
improving on Claudius Ptolemy's Geographia.
1about 780-850 AD2The Compendious Book on Calculation by Completion and Balancing”
3"Al-Khwarizmi Concerning the Hindu Art of Reckoning”.
4"The Image of the Earth", or more simply, "Geography"